Such a method is known from U.S. Pat. No. 4,804,905, for example. For this purpose, a capacitive sensor, which can sense the distance from the blade airfoil tips for each passing rotor blade during operation of the gas turbine, is arranged in a housing of the turbine which delimits the flow path. If an excessively large radial gap is detected, the conical housing is shifted axially by means of hydraulic actuators for reducing the gap. It is disadvantageous, however, that only one measuring point per sensor can be sensed on the circumference of the housing so that at least four sensors are required per stage. Also, when using four sensors, only a rough statement can then be made about the gap distribution on the circumference. Therefore, the gap between the measuring points can only be interpolated or estimated, for example. A further disadvantage of said solution is that on account of the secure fastening of the sensors the construction is comparatively complex and expensive since the detecting of the radial gaps is carried out during operation of the gas turbine and cooling of the sensors is required so that these can permanently withstand the temperatures which meanwhile occur.
Also, it is known from EP 0 806 680 A2 and from GB 2460248 A to carry out this measuring not during operation of the turbomachine but before it or after it.